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MathCode (Website)

MathCode (Website)

AI opensource Math-ai-org.github.io
MathCode is a new terminal assistant that translates natural language math into Lean 4 formal proofs using a persistent REPL and dependency graphs.
What: MathCode provides a math formalization pipeline that utilizes the AUTOLEAN project's logic. Features include a persistent Lean 4 REPL for ~0.4s compilation checks, an Obsidian-integrated knowledge graph for theorem dependencies, and a parallel 'Tree-of-Subgoals' solver.
Why it matters: Bridging the gap between natural language prompts and verifiable formal logic is the next frontier for ensuring the correctness of AI-generated code.
Takeaway: Install the tool via `git clone https://github.com/math-ai-org/mathcode.git` if you need to generate formal proofs for mathematical problems.
Decoder
  • Lean 4: A theorem prover and functional programming language designed for formal mathematical verification.
  • REPL (Read-Eval-Print Loop): An interactive programming environment that takes input, evaluates it, and prints the result.
  • LSP (Language Server Protocol): A standardized way for editors to provide features like autocomplete and error checking for a language.
Original article

Overview

MathCode is a terminal AI coding assistant with a built-in math formalization engine. Give it a math problem in plain language and it will automatically convert it into a Lean 4 theorem and attempt a formal proof — with a persistent Lean REPL, reusable theorem and axiom libraries, agentic proving, and an Obsidian knowledge graph.

Quick Start

Requires macOS (arm64) or Linux (x86_64), plus the codex CLI for the default backend.

git clone https://github.com/math-ai-org/mathcode.git
cd mathcode
bash setup.sh
codex auth login
mathcode

setup.sh prepares the release checkout, downloads the bundled runtime and Lean toolchain, and installs a user-local mathcode launcher. Try it with:

mathcode -p "prove that the square of an even number is even"

Outputs are written to LeanFormalizations/. A browser UI is available via ./run webui.

Features

Persistent Lean REPL

A persistent Lean language server brings compile checks to ~0.4s after a one-time warmup, instead of ~30s.

Theorem Library

Every proved theorem is auto-named, stored, and made importable so the prover and planner can reuse it.

Axiom Library

Store conversational assumptions as persistent, compile-checked, consistency-reviewed Lean declarations.

Lean LSP Integration

Searches leansearch.net and Loogle for verified Mathlib lemmas and uses structured LSP diagnostics for repairs.

Obsidian Theorem Graph

Generates an Obsidian vault that visualizes theorem-to-lemma dependencies as a knowledge graph.

Agent-Mode Proving

Each proof becomes an interactive session where the agent writes candidates, reads errors, and recompiles.

Tree-of-Subgoals

Decomposes complex theorems into independent subgoals and proves them in parallel, then stitches them back.

Multi-Planner

Runs multiple planners in parallel for diverse proof strategies; the prover picks the best approach.

Citation

If you use MathCode in research, please cite:

@misc{mathcode2026,
  title   = {MathCode: A Frontier Mathematical Coding Agent},
  author  = {Team Math-AI},
  journal = {math-ai-org.github.io},
  year    = {2026},
  month   = {April},
  url     = {https://github.com/math-ai-org/mathcode}
}

The math formalization and proving pipeline is based on the AUTOLEAN project.

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